Cochran's team faced a midnight Wednesday deadline to file arguments with the Mississippi Supreme Court, and attorney Mark Garriga said the papers could be filed late in the day. The attorneys were expected to say a circuit judge correctly dismissed a lawsuit by state Sen. Chris McDaniel.

Judge Hollis McGehee ruled last month that McDaniel waited too long to challenge results of the June 24 Republican primary runoff. In doing so, McGehee agreed with Cochran's attorneys, who cited a 1959 Mississippi Supreme Court ruling that said a candidate had 20 days to appeal a loss in a multi-county election.

McDaniel's attorneys argue that Mississippi election laws were substantially rewritten in 1986 and current law does not include a timetable for challenging a loss.

Certified results show Cochran defeated McDaniel by 7,667 votes on June 24. The runoff came three weeks after the tea party-backed McDaniel had led a three-person primary.

McDaniel filed a lawsuit in mid-August, claiming the runoff was tainted by the participation of Democrats. The state does not require voters to register by party, and as chairman of the state Senate election committee the past three years, McDaniel has not pushed to restrict who can vote in party primaries.

The lawsuit asked a judge to either declare McDaniel winner of the Republican nomination or order a new runoff.

Cochran and his campaign say the six-term incumbent won the runoff fairly by telling voters about his record in Washington.

McDaniel is asking the state Supreme Court to revive his lawsuit that claims election fraud. Justices are scheduled to oral arguments Oct. 2.

Officials have set a Nov. 4 general election ballot with Cochran as the Republican nominee, former U.S. Rep. Travis Childers as the Democrat and Shawn O'Hara as the Reform Party candidate.

State law says a new primary could be ordered even after someone wins the general election. If that were to happen, a new general election also would have to be held.